• Publications
  • Influence
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomialsExpand
  • 1,006
  • 123
  • PDF
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties
We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toricExpand
  • 338
  • 32
  • PDF
New Trends in Algebraic Geometry: Birational Calabi–Yau n -folds have equal Betti numbers
Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local numberExpand
  • 136
  • 22
  • PDF
Tamagawa numbers of polarized algebraic varieties
Let ${\cal L} = (L, \| \cdot \|_v)$ be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety $V$ defined over a number field. Denote by $N(V,{\cal L},B)$ the number ofExpand
  • 91
  • 22
  • PDF
On the Hodge structure of projective hypersurfaces in toric varieties
This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toricExpand
  • 187
  • 19
  • PDF
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural KawamataExpand
  • 172
  • 18
  • PDF
Stringy Hodge numbers of varieties with Gorenstein canonical singularities
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functionsExpand
  • 178
  • 17
  • PDF
Mirror duality and string-theoretic Hodge numbers
Abstract. We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi–Yau complete intersections in Gorenstein toric Fano varieties. The proof is based onExpand
  • 169
  • 16
  • PDF
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
Abstract We propose a new higher dimensional version of the McKay correspondence which enables us to understand the “Hodge numbers” assigned to singular Gorenstein varieties by physicists. OurExpand
  • 204
  • 16
  • PDF